LMFDB - Embedded newform 1150.2.e.f.1057.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.12877254853348294656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 26x^{12} + 12x^{10} + 35x^{8} + 180x^{6} + 686x^{4} + 632x^{2} + 169 $ x^16 - 4x^14 + 26x^12 + 12x^10 + 35x^8 + 180x^6 + 686x^4 + 632*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.4
Root			$1.46009 + 0.752986i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.f.643.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.22474 - 1.22474i) q^{3} +1.00000i q^{4} -1.73205 q^{6} +(1.50597 - 1.50597i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 - 1.22474i) q^{3} +1.00000i q^{4} -1.73205 q^{6} +(1.50597 - 1.50597i) q^{7} +(0.707107 - 0.707107i) q^{8} +5.03908i q^{11} +(1.22474 + 1.22474i) q^{12} +(-3.34607 + 3.34607i) q^{13} -2.12976 q^{14} -1.00000 q^{16} +(5.06914 - 5.06914i) q^{17} +5.03908 q^{19} -3.68886i q^{21} +(3.56317 - 3.56317i) q^{22} +(3.80969 + 2.91312i) q^{23} -1.73205i q^{24} +4.73205 q^{26} +(3.67423 + 3.67423i) q^{27} +(1.50597 + 1.50597i) q^{28} -5.46410i q^{29} +4.73205 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.17158 + 6.17158i) q^{33} -7.16884 q^{34} +(4.11439 - 4.11439i) q^{37} +(-3.56317 - 3.56317i) q^{38} +8.19615i q^{39} -11.9282 q^{41} +(-2.60842 + 2.60842i) q^{42} +(-1.10245 - 1.10245i) q^{43} -5.03908 q^{44} +(-0.633975 - 4.75374i) q^{46} +(-3.34607 - 3.34607i) q^{47} +(-1.22474 + 1.22474i) q^{48} +2.46410i q^{49} -12.4168i q^{51} +(-3.34607 - 3.34607i) q^{52} +(9.73475 + 9.73475i) q^{53} -5.19615i q^{54} -2.12976i q^{56} +(6.17158 - 6.17158i) q^{57} +(-3.86370 + 3.86370i) q^{58} -0.535898i q^{59} -3.68886i q^{61} +(-3.34607 - 3.34607i) q^{62} -1.00000i q^{64} -8.72794i q^{66} +(-2.05719 + 2.05719i) q^{67} +(5.06914 + 5.06914i) q^{68} +(8.23373 - 1.09808i) q^{69} +1.07180 q^{71} +(0.568406 - 0.568406i) q^{73} -5.81863 q^{74} +5.03908i q^{76} +(7.58871 + 7.58871i) q^{77} +(5.79555 - 5.79555i) q^{78} +2.70043 q^{79} +9.00000 q^{81} +(8.43451 + 8.43451i) q^{82} +(-11.3884 - 11.3884i) q^{83} +3.68886 q^{84} +1.55910i q^{86} +(-6.69213 - 6.69213i) q^{87} +(3.56317 + 3.56317i) q^{88} -12.4168 q^{89} +10.0782i q^{91} +(-2.91312 + 3.80969i) q^{92} +(5.79555 - 5.79555i) q^{93} +4.73205i q^{94} +1.73205 q^{96} +(1.10245 - 1.10245i) q^{97} +(1.74238 - 1.74238i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 16 q^{16} + 48 q^{26} + 48 q^{31} - 80 q^{41} - 24 q^{46} + 128 q^{71} + 144 q^{81}+O(q^{100}) $ 16 * q - 16 * q^16 + 48 * q^26 + 48 * q^31 - 80 * q^41 - 24 * q^46 + 128 * q^71 + 144 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−1.73205			−0.707107
$7$	1.50597	−	1.50597i	0.569204	−	0.569204i	−0.362702	−	0.931905i	$-0.618146\pi$
$7$	1.50597	−	1.50597i	0.569204	−	0.569204i	0.931905	+	0.362702i	$0.118146\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			5.03908i			1.51934i	0.650309	+	0.759670i	$0.274639\pi$
$11$			5.03908i			1.51934i	−0.650309	+	0.759670i	$0.725361\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	−3.34607	+	3.34607i	−0.928032	+	0.928032i	−0.997579	−	0.0695471i	$-0.977845\pi$
$13$	−3.34607	+	3.34607i	−0.928032	+	0.928032i	0.0695471	+	0.997579i	$0.477845\pi$
$14$	−2.12976			−0.569204
$15$		0			0
$16$	−1.00000			−0.250000
$17$	5.06914	−	5.06914i	1.22945	−	1.22945i	0.265273	−	0.964173i	$-0.414538\pi$
$17$	5.06914	−	5.06914i	1.22945	−	1.22945i	0.964173	−	0.265273i	$-0.0854621\pi$
$18$		0			0
$19$	5.03908			1.15604			0.578022	−	0.816021i	$-0.303825\pi$
$19$	5.03908			1.15604			0.578022	+	0.816021i	$0.303825\pi$
$20$		0			0
$21$		−	3.68886i		−	0.804975i
$22$	3.56317	−	3.56317i	0.759670	−	0.759670i
$23$	3.80969	+	2.91312i	0.794376	+	0.607427i
$23$	3.80969	+	2.91312i	0.794376	+	0.607427i
$24$		−	1.73205i		−	0.353553i
$25$		0			0
$26$	4.73205			0.928032
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$	1.50597	+	1.50597i	0.284602	+	0.284602i
$29$		−	5.46410i		−	1.01466i	−0.861752	−	0.507329i	$-0.830633\pi$
$29$		−	5.46410i		−	1.01466i	0.861752	−	0.507329i	$-0.169367\pi$
$30$		0			0
$31$	4.73205			0.849901			0.424951	−	0.905216i	$-0.360291\pi$
$31$	4.73205			0.849901			0.424951	+	0.905216i	$0.360291\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	6.17158	+	6.17158i	1.07433	+	1.07433i
$34$	−7.16884			−1.22945
$35$		0			0
$36$		0			0
$37$	4.11439	−	4.11439i	0.676402	−	0.676402i	−0.282783	−	0.959184i	$-0.591257\pi$
$37$	4.11439	−	4.11439i	0.676402	−	0.676402i	0.959184	+	0.282783i	$0.0912575\pi$
$38$	−3.56317	−	3.56317i	−0.578022	−	0.578022i
$39$			8.19615i			1.31243i
$40$		0			0
$41$	−11.9282			−1.86287			−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−11.9282			−1.86287			−0.931436	+	0.363905i	$0.881443\pi$
$42$	−2.60842	+	2.60842i	−0.402488	+	0.402488i
$43$	−1.10245	−	1.10245i	−0.168122	−	0.168122i	0.618032	−	0.786153i	$-0.287930\pi$
$43$	−1.10245	−	1.10245i	−0.168122	−	0.168122i	−0.786153	+	0.618032i	$0.787930\pi$
$44$	−5.03908			−0.759670
$45$		0			0
$46$	−0.633975	−	4.75374i	−0.0934745	−	0.700901i
$47$	−3.34607	−	3.34607i	−0.488074	−	0.488074i	0.419624	−	0.907698i	$-0.362162\pi$
$47$	−3.34607	−	3.34607i	−0.488074	−	0.488074i	−0.907698	+	0.419624i	$0.862162\pi$
$48$	−1.22474	+	1.22474i	−0.176777	+	0.176777i
$49$			2.46410i			0.352015i
$50$		0			0
$51$		−	12.4168i		−	1.73870i
$52$	−3.34607	−	3.34607i	−0.464016	−	0.464016i
$53$	9.73475	+	9.73475i	1.33717	+	1.33717i	0.898789	+	0.438382i	$0.144448\pi$
$53$	9.73475	+	9.73475i	1.33717	+	1.33717i	0.438382	+	0.898789i	$0.355552\pi$
$54$		−	5.19615i		−	0.707107i
$55$		0			0
$56$		−	2.12976i		−	0.284602i
$57$	6.17158	−	6.17158i	0.817446	−	0.817446i
$58$	−3.86370	+	3.86370i	−0.507329	+	0.507329i
$59$		−	0.535898i		−	0.0697680i	−0.999391	−	0.0348840i	$-0.988894\pi$
$59$		−	0.535898i		−	0.0697680i	0.999391	−	0.0348840i	$-0.0111062\pi$
$60$		0			0
$61$		−	3.68886i		−	0.472310i	−0.971715	−	0.236155i	$-0.924113\pi$
$61$		−	3.68886i		−	0.472310i	0.971715	−	0.236155i	$-0.0758874\pi$
$62$	−3.34607	−	3.34607i	−0.424951	−	0.424951i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		−	8.72794i		−	1.07433i
$67$	−2.05719	+	2.05719i	−0.251326	+	0.251326i	−0.821514	−	0.570188i	$-0.806870\pi$
$67$	−2.05719	+	2.05719i	−0.251326	+	0.251326i	0.570188	+	0.821514i	$0.306870\pi$
$68$	5.06914	+	5.06914i	0.614723	+	0.614723i
$69$	8.23373	−	1.09808i	0.991224	−	0.132193i
$70$		0			0
$71$	1.07180			0.127199			0.0635994	−	0.997976i	$-0.479742\pi$
$71$	1.07180			0.127199			0.0635994	+	0.997976i	$0.479742\pi$
$72$		0			0
$73$	0.568406	−	0.568406i	0.0665269	−	0.0665269i	−0.673061	−	0.739587i	$-0.735021\pi$
$73$	0.568406	−	0.568406i	0.0665269	−	0.0665269i	0.739587	+	0.673061i	$0.235021\pi$
$74$	−5.81863			−0.676402
$75$		0			0
$76$			5.03908i			0.578022i
$77$	7.58871	+	7.58871i	0.864813	+	0.864813i
$78$	5.79555	−	5.79555i	0.656217	−	0.656217i
$79$	2.70043			0.303823			0.151911	−	0.988394i	$-0.451457\pi$
$79$	2.70043			0.303823			0.151911	+	0.988394i	$0.451457\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$	8.43451	+	8.43451i	0.931436	+	0.931436i
$83$	−11.3884	−	11.3884i	−1.25004	−	1.25004i	−0.955700	−	0.294341i	$-0.904900\pi$
$83$	−11.3884	−	11.3884i	−1.25004	−	1.25004i	−0.294341	−	0.955700i	$-0.595100\pi$
$84$	3.68886			0.402488
$85$		0			0
$86$			1.55910i			0.168122i
$87$	−6.69213	−	6.69213i	−0.717472	−	0.717472i
$88$	3.56317	+	3.56317i	0.379835	+	0.379835i
$89$	−12.4168			−1.31618			−0.658089	−	0.752940i	$-0.728635\pi$
$89$	−12.4168			−1.31618			−0.658089	+	0.752940i	$0.728635\pi$
$90$		0			0
$91$			10.0782i			1.05648i
$92$	−2.91312	+	3.80969i	−0.303713	+	0.397188i
$93$	5.79555	−	5.79555i	0.600971	−	0.600971i
$94$			4.73205i			0.488074i
$95$		0			0
$96$	1.73205			0.176777
$97$	1.10245	−	1.10245i	0.111937	−	0.111937i	−0.648920	−	0.760857i	$-0.724779\pi$
$97$	1.10245	−	1.10245i	0.111937	−	0.111937i	0.760857	+	0.648920i	$0.224779\pi$
$98$	1.74238	−	1.74238i	0.176007	−	0.176007i
$99$		0			0
$100$		0			0
$101$	17.1244			1.70394			0.851969	−	0.523593i	$-0.175409\pi$
$101$	17.1244			1.70394			0.851969	+	0.523593i	$0.175409\pi$
$102$	−8.78000	+	8.78000i	−0.869350	+	0.869350i
$103$	3.41547	+	3.41547i	0.336536	+	0.336536i	0.855062	−	0.518526i	$-0.173519\pi$
$103$	3.41547	+	3.41547i	0.336536	+	0.336536i	−0.518526	+	0.855062i	$0.673519\pi$
$104$			4.73205i			0.464016i
$105$		0			0
$106$		−	13.7670i		−	1.33717i
$107$	5.06914	−	5.06914i	0.490052	−	0.490052i	−0.418271	−	0.908323i	$-0.637364\pi$
$107$	5.06914	−	5.06914i	0.490052	−	0.490052i	0.908323	+	0.418271i	$0.137364\pi$
$108$	−3.67423	+	3.67423i	−0.353553	+	0.353553i
$109$	10.0782			0.965312			0.482656	−	0.875810i	$-0.339672\pi$
$109$	10.0782			0.965312			0.482656	+	0.875810i	$0.339672\pi$
$110$		0			0
$111$		−	10.0782i		−	0.956576i
$112$	−1.50597	+	1.50597i	−0.142301	+	0.142301i
$113$	−8.08108	−	8.08108i	−0.760204	−	0.760204i	0.216155	−	0.976359i	$-0.430648\pi$
$113$	−8.08108	−	8.08108i	−0.760204	−	0.760204i	−0.976359	+	0.216155i	$0.930648\pi$
$114$	−8.72794			−0.817446
$115$		0			0
$116$	5.46410			0.507329
$117$		0			0
$118$	−0.378937	+	0.378937i	−0.0348840	+	0.0348840i
$119$		−	15.2679i		−	1.39961i
$120$		0			0
$121$	−14.3923			−1.30839
$122$	−2.60842	+	2.60842i	−0.236155	+	0.236155i
$123$	−14.6090	+	14.6090i	−1.31725	+	1.31725i
$124$			4.73205i			0.424951i
$125$		0			0
$126$		0			0
$127$	−5.79555	−	5.79555i	−0.514272	−	0.514272i	0.401560	−	0.915833i	$-0.368468\pi$
$127$	−5.79555	−	5.79555i	−0.514272	−	0.514272i	−0.915833	+	0.401560i	$0.868468\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−2.70043			−0.237760
$130$		0			0
$131$	−14.0000			−1.22319			−0.611593	−	0.791173i	$-0.709471\pi$
$131$	−14.0000			−1.22319			−0.611593	+	0.791173i	$0.709471\pi$
$132$	−6.17158	+	6.17158i	−0.537167	+	0.537167i
$133$	7.58871	−	7.58871i	0.658024	−	0.658024i
$134$	2.90931			0.251326
$135$		0			0
$136$		−	7.16884i		−	0.614723i
$137$	−5.06914	+	5.06914i	−0.433086	+	0.433086i	−0.889677	−	0.456591i	$-0.849070\pi$
$137$	−5.06914	+	5.06914i	−0.433086	+	0.433086i	0.456591	+	0.889677i	$0.349070\pi$
$138$	−6.59858	−	5.04567i	−0.561708	−	0.429516i
$139$			15.9282i			1.35101i	0.737354	+	0.675506i	$0.236075\pi$
$139$			15.9282i			1.35101i	−0.737354	+	0.675506i	$0.763925\pi$
$140$		0			0
$141$	−8.19615			−0.690241
$142$	−0.757875	−	0.757875i	−0.0635994	−	0.0635994i
$143$	−16.8611	−	16.8611i	−1.40999	−	1.40999i
$144$		0			0
$145$		0			0
$146$	−0.803848			−0.0665269
$147$	3.01790	+	3.01790i	0.248912	+	0.248912i
$148$	4.11439	+	4.11439i	0.338201	+	0.338201i
$149$	−13.7670			−1.12784			−0.563919	−	0.825830i	$-0.690707\pi$
$149$	−13.7670			−1.12784			−0.563919	+	0.825830i	$0.690707\pi$
$150$		0			0
$151$	2.19615			0.178720			0.0893602	−	0.995999i	$-0.471518\pi$
$151$	2.19615			0.178720			0.0893602	+	0.995999i	$0.471518\pi$
$152$	3.56317	−	3.56317i	0.289011	−	0.289011i
$153$		0			0
$154$		−	10.7321i		−	0.864813i
$155$		0			0
$156$	−8.19615			−0.656217
$157$	9.33123	−	9.33123i	0.744713	−	0.744713i	−0.228768	−	0.973481i	$-0.573470\pi$
$157$	9.33123	−	9.33123i	0.744713	−	0.744713i	0.973481	+	0.228768i	$0.0734697\pi$
$158$	−1.90949	−	1.90949i	−0.151911	−	0.151911i
$159$	23.8452			1.89105
$160$		0			0
$161$	10.1244	−	1.35022i	0.797911	−	0.106412i
$162$	−6.36396	−	6.36396i	−0.500000	−	0.500000i
$163$	11.5032	−	11.5032i	0.900998	−	0.900998i	−0.0945242	−	0.995523i	$-0.530133\pi$
$163$	11.5032	−	11.5032i	0.900998	−	0.900998i	0.995523	+	0.0945242i	$0.0301330\pi$
$164$		−	11.9282i		−	0.931436i
$165$		0			0
$166$			16.1057i			1.25004i
$167$	−6.93237	−	6.93237i	−0.536443	−	0.536443i	0.386040	−	0.922482i	$-0.373843\pi$
$167$	−6.93237	−	6.93237i	−0.536443	−	0.536443i	−0.922482	+	0.386040i	$0.873843\pi$
$168$	−2.60842	−	2.60842i	−0.201244	−	0.201244i
$169$		−	9.39230i		−	0.722485i
$170$		0			0
$171$		0			0
$172$	1.10245	−	1.10245i	0.0840608	−	0.0840608i
$173$	−13.3843	+	13.3843i	−1.01759	+	1.01759i	−0.0177439	+	0.999843i	$0.505648\pi$
$173$	−13.3843	+	13.3843i	−1.01759	+	1.01759i	−0.999843	+	0.0177439i	$0.994352\pi$
$174$			9.46410i			0.717472i
$175$		0			0
$176$		−	5.03908i		−	0.379835i
$177$	−0.656339	−	0.656339i	−0.0493334	−	0.0493334i
$178$	8.78000	+	8.78000i	0.658089	+	0.658089i
$179$			1.00000i			0.0747435i	0.999301	+	0.0373718i	$0.0118986\pi$
$179$			1.00000i			0.0747435i	−0.999301	+	0.0373718i	$0.988101\pi$
$180$		0			0
$181$			17.4559i			1.29749i	0.761008	+	0.648743i	$0.224705\pi$
$181$			17.4559i			1.29749i	−0.761008	+	0.648743i	$0.775295\pi$
$182$	7.12633	−	7.12633i	0.528239	−	0.528239i
$183$	−4.51791	−	4.51791i	−0.333974	−	0.333974i
$184$	4.75374	−	0.633975i	0.350451	−	0.0467372i
$185$		0			0
$186$	−8.19615			−0.600971
$187$	25.5438	+	25.5438i	1.86795	+	1.86795i
$188$	3.34607	−	3.34607i	0.244037	−	0.244037i
$189$	11.0666			0.804975
$190$		0			0
$191$			11.0666i			0.800750i	0.916351	+	0.400375i	$0.131120\pi$
$191$			11.0666i			0.800750i	−0.916351	+	0.400375i	$0.868880\pi$
$192$	−1.22474	−	1.22474i	−0.0883883	−	0.0883883i
$193$	11.0227	−	11.0227i	0.793432	−	0.793432i	−0.188619	−	0.982050i	$-0.560401\pi$
$193$	11.0227	−	11.0227i	0.793432	−	0.793432i	0.982050	+	0.188619i	$0.0604011\pi$
$194$	−1.55910			−0.111937
$195$		0			0
$196$	−2.46410			−0.176007
$197$	4.48288	+	4.48288i	0.319392	+	0.319392i	0.848533	−	0.529142i	$-0.177486\pi$
$197$	4.48288	+	4.48288i	0.319392	+	0.319392i	−0.529142	+	0.848533i	$0.677486\pi$
$198$		0			0
$199$	13.7670			0.975918			0.487959	−	0.872867i	$-0.337742\pi$
$199$	13.7670			0.975918			0.487959	+	0.872867i	$0.337742\pi$
$200$		0			0
$201$			5.03908i			0.355429i
$202$	−12.1087	−	12.1087i	−0.851969	−	0.851969i
$203$	−8.22878	−	8.22878i	−0.577547	−	0.577547i
$204$	12.4168			0.869350
$205$		0			0
$206$		−	4.83020i		−	0.336536i
$207$		0			0
$208$	3.34607	−	3.34607i	0.232008	−	0.232008i
$209$			25.3923i			1.75642i
$210$		0			0
$211$	0.464102			0.0319501			0.0159750	−	0.999872i	$-0.494915\pi$
$211$	0.464102			0.0319501			0.0159750	+	0.999872i	$0.494915\pi$
$212$	−9.73475	+	9.73475i	−0.668585	+	0.668585i
$213$	1.31268	−	1.31268i	0.0899432	−	0.0899432i
$214$	−7.16884			−0.490052
$215$		0			0
$216$	5.19615			0.353553
$217$	7.12633	−	7.12633i	0.483767	−	0.483767i
$218$	−7.12633	−	7.12633i	−0.482656	−	0.482656i
$219$		−	1.39230i		−	0.0940832i
$220$		0			0
$221$			33.9233i			2.28193i
$222$	−7.12633	+	7.12633i	−0.478288	+	0.478288i
$223$	−3.10583	+	3.10583i	−0.207982	+	0.207982i	−0.803409	−	0.595427i	$-0.796983\pi$
$223$	−3.10583	+	3.10583i	−0.207982	+	0.207982i	0.595427	+	0.803409i	$0.296983\pi$
$224$	2.12976			0.142301
$225$		0			0
$226$			11.4284i			0.760204i
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$	6.17158	+	6.17158i	0.408723	+	0.408723i
$229$	6.38929			0.422216			0.211108	−	0.977463i	$-0.432293\pi$
$229$	6.38929			0.422216			0.211108	+	0.977463i	$0.432293\pi$
$230$		0			0
$231$	18.5885			1.22303
$232$	−3.86370	−	3.86370i	−0.253665	−	0.253665i
$233$	1.31268	−	1.31268i	0.0859964	−	0.0859964i	−0.662800	−	0.748796i	$-0.730632\pi$
$233$	1.31268	−	1.31268i	0.0859964	−	0.0859964i	0.748796	+	0.662800i	$0.230632\pi$
$234$		0			0
$235$		0			0
$236$	0.535898			0.0348840
$237$	3.30734	−	3.30734i	0.214835	−	0.214835i
$238$	−10.7961	+	10.7961i	−0.699805	+	0.699805i
$239$		−	6.73205i		−	0.435460i	−0.976009	−	0.217730i	$-0.930135\pi$
$239$		−	6.73205i		−	0.435460i	0.976009	−	0.217730i	$-0.0698652\pi$
$240$		0			0
$241$			12.4168i			0.799836i	0.916551	+	0.399918i	$0.130961\pi$
$241$			12.4168i			0.799836i	−0.916551	+	0.399918i	$0.869039\pi$
$242$	10.1769	+	10.1769i	0.654196	+	0.654196i
$243$		0			0
$244$	3.68886			0.236155
$245$		0			0
$246$	20.6603			1.31725
$247$	−16.8611	+	16.8611i	−1.07285	+	1.07285i
$248$	3.34607	−	3.34607i	0.212475	−	0.212475i
$249$	−27.8958			−1.76783
$250$		0			0
$251$			2.33864i			0.147614i	0.997273	+	0.0738070i	$0.0235149\pi$
$251$			2.33864i			0.147614i	−0.997273	+	0.0738070i	$0.976485\pi$
$252$		0			0
$253$	−14.6794	+	19.1973i	−0.922887	+	1.20693i
$254$			8.19615i			0.514272i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−19.4201	−	19.4201i	−1.21139	−	1.21139i	−0.970570	−	0.240820i	$-0.922584\pi$
$257$	−19.4201	−	19.4201i	−1.21139	−	1.21139i	−0.240820	−	0.970570i	$-0.577416\pi$
$258$	1.90949	+	1.90949i	0.118880	+	0.118880i
$259$		−	12.3923i		−	0.770020i
$260$		0			0
$261$		0			0
$262$	9.89949	+	9.89949i	0.611593	+	0.611593i
$263$	0.698924	+	0.698924i	0.0430975	+	0.0430975i	0.728327	−	0.685230i	$-0.240298\pi$
$263$	0.698924	+	0.698924i	0.0430975	+	0.0430975i	−0.685230	+	0.728327i	$0.740298\pi$
$264$	8.72794			0.537167
$265$		0			0
$266$	−10.7321			−0.658024
$267$	−15.2074	+	15.2074i	−0.930678	+	0.930678i
$268$	−2.05719	−	2.05719i	−0.125663	−	0.125663i
$269$			21.6603i			1.32065i	0.750980	+	0.660324i	$0.229581\pi$
$269$			21.6603i			1.32065i	−0.750980	+	0.660324i	$0.770419\pi$
$270$		0			0
$271$	−22.7846			−1.38407			−0.692033	−	0.721866i	$-0.743285\pi$
$271$	−22.7846			−1.38407			−0.692033	+	0.721866i	$0.743285\pi$
$272$	−5.06914	+	5.06914i	−0.307362	+	0.307362i
$273$	12.3432	+	12.3432i	0.747043	+	0.747043i
$274$	7.16884			0.433086
$275$		0			0
$276$	1.09808	+	8.23373i	0.0660964	+	0.495612i
$277$	−18.2832	−	18.2832i	−1.09853	−	1.09853i	−0.994582	−	0.103951i	$-0.966851\pi$
$277$	−18.2832	−	18.2832i	−1.09853	−	1.09853i	−0.103951	−	0.994582i	$-0.533149\pi$
$278$	11.2629	−	11.2629i	0.675506	−	0.675506i
$279$		0			0
$280$		0			0
$281$			2.70043i			0.161094i	0.996751	+	0.0805472i	$0.0256668\pi$
$281$			2.70043i			0.161094i	−0.996751	+	0.0805472i	$0.974333\pi$
$282$	5.79555	+	5.79555i	0.345120	+	0.345120i
$283$	−22.6291	−	22.6291i	−1.34516	−	1.34516i	−0.890834	−	0.454329i	$-0.849879\pi$
$283$	−22.6291	−	22.6291i	−1.34516	−	1.34516i	−0.454329	−	0.890834i	$-0.650121\pi$
$284$			1.07180i			0.0635994i
$285$		0			0
$286$			23.8452i			1.40999i
$287$	−17.9635	+	17.9635i	−1.06035	+	1.06035i
$288$		0			0
$289$		−	34.3923i		−	2.02308i
$290$		0			0
$291$		−	2.70043i		−	0.158302i
$292$	0.568406	+	0.568406i	0.0332634	+	0.0332634i
$293$	8.92770	+	8.92770i	0.521562	+	0.521562i	0.918043	−	0.396481i	$-0.129769\pi$
$293$	8.92770	+	8.92770i	0.521562	+	0.521562i	−0.396481	+	0.918043i	$0.629769\pi$
$294$		−	4.26795i		−	0.248912i
$295$		0			0
$296$		−	5.81863i		−	0.338201i
$297$	−18.5148	+	18.5148i	−1.07433	+	1.07433i
$298$	9.73475	+	9.73475i	0.563919	+	0.563919i
$299$	−22.4950	+	3.00000i	−1.30092	+	0.173494i
$300$		0			0
$301$	−3.32051			−0.191391
$302$	−1.55291	−	1.55291i	−0.0893602	−	0.0893602i
$303$	20.9730	−	20.9730i	1.20487	−	1.20487i
$304$	−5.03908			−0.289011
$305$		0			0
$306$		0			0
$307$	4.15471	+	4.15471i	0.237122	+	0.237122i	0.815657	−	0.578535i	$-0.196376\pi$
$307$	4.15471	+	4.15471i	0.237122	+	0.237122i	−0.578535	+	0.815657i	$0.696376\pi$
$308$	−7.58871	+	7.58871i	−0.432407	+	0.432407i
$309$	8.36615			0.475934
$310$		0			0
$311$	−30.7846			−1.74564			−0.872818	−	0.488047i	$-0.837710\pi$
$311$	−30.7846			−1.74564			−0.872818	+	0.488047i	$0.837710\pi$
$312$	5.79555	+	5.79555i	0.328109	+	0.328109i
$313$	6.31928	+	6.31928i	0.357187	+	0.357187i	0.862775	−	0.505588i	$-0.168724\pi$
$313$	6.31928	+	6.31928i	0.357187	+	0.357187i	−0.505588	+	0.862775i	$0.668724\pi$
$314$	−13.1963			−0.744713
$315$		0			0
$316$			2.70043i			0.151911i
$317$	12.9038	+	12.9038i	0.724749	+	0.724749i	0.969569	−	0.244820i	$-0.0787288\pi$
$317$	12.9038	+	12.9038i	0.724749	+	0.724749i	−0.244820	+	0.969569i	$0.578729\pi$
$318$	−16.8611	−	16.8611i	−0.945523	−	0.945523i
$319$	27.5340			1.54161
$320$		0			0
$321$		−	12.4168i		−	0.693038i
$322$	−8.11375	−	6.20425i	−0.452161	−	0.345750i
$323$	25.5438	−	25.5438i	1.42129	−	1.42129i
$324$			9.00000i			0.500000i
$325$		0			0
$326$	−16.2679			−0.900998
$327$	12.3432	−	12.3432i	0.682579	−	0.682579i
$328$	−8.43451	+	8.43451i	−0.465718	+	0.465718i
$329$	−10.0782			−0.555627
$330$		0			0
$331$	19.7846			1.08746			0.543730	−	0.839260i	$-0.317011\pi$
$331$	19.7846			1.08746			0.543730	+	0.839260i	$0.317011\pi$
$332$	11.3884	−	11.3884i	0.625021	−	0.625021i
$333$		0			0
$334$			9.80385i			0.536443i
$335$		0			0
$336$			3.68886i			0.201244i
$337$	−14.1050	+	14.1050i	−0.768346	+	0.768346i	−0.977815	−	0.209469i	$-0.932826\pi$
$337$	−14.1050	+	14.1050i	−0.768346	+	0.768346i	0.209469	+	0.977815i	$0.432826\pi$
$338$	−6.64136	+	6.64136i	−0.361242	+	0.361242i
$339$	−19.7945			−1.07509
$340$		0			0
$341$			23.8452i			1.29129i
$342$		0			0
$343$	14.2527	+	14.2527i	0.769572	+	0.769572i
$344$	−1.55910			−0.0840608
$345$		0			0
$346$	18.9282			1.01759
$347$	−25.5438	−	25.5438i	−1.37126	−	1.37126i	−0.858577	−	0.512685i	$-0.828651\pi$
$347$	−25.5438	−	25.5438i	−1.37126	−	1.37126i	−0.512685	−	0.858577i	$-0.671349\pi$
$348$	6.69213	−	6.69213i	0.358736	−	0.358736i
$349$			10.7846i			0.577287i	0.957437	+	0.288643i	$0.0932042\pi$
$349$			10.7846i			0.577287i	−0.957437	+	0.288643i	$0.906796\pi$
$350$		0			0
$351$	−24.5885			−1.31243
$352$	−3.56317	+	3.56317i	−0.189917	+	0.189917i
$353$	−14.5211	+	14.5211i	−0.772879	+	0.772879i	−0.978609	−	0.205730i	$-0.934043\pi$
$353$	−14.5211	+	14.5211i	−0.772879	+	0.772879i	0.205730	+	0.978609i	$0.434043\pi$
$354$			0.928203i			0.0493334i
$355$		0			0
$356$		−	12.4168i		−	0.658089i
$357$	−18.6993	−	18.6993i	−0.989674	−	0.989674i
$358$	0.707107	−	0.707107i	0.0373718	−	0.0373718i
$359$	−11.0666			−0.584072			−0.292036	−	0.956407i	$-0.594333\pi$
$359$	−11.0666			−0.584072			−0.292036	+	0.956407i	$0.594333\pi$
$360$		0			0
$361$	6.39230			0.336437
$362$	12.3432	−	12.3432i	0.648743	−	0.648743i
$363$	−17.6269	+	17.6269i	−0.925172	+	0.925172i
$364$	−10.0782			−0.528239
$365$		0			0
$366$			6.38929i			0.333974i
$367$	−16.0540	+	16.0540i	−0.838014	+	0.838014i	−0.988597	−	0.150583i	$-0.951885\pi$
$367$	−16.0540	+	16.0540i	−0.838014	+	0.838014i	0.150583	+	0.988597i	$0.451885\pi$
$368$	−3.80969	−	2.91312i	−0.198594	−	0.151857i
$369$		0			0
$370$		0			0
$371$	29.3205			1.52224
$372$	5.79555	+	5.79555i	0.300486	+	0.300486i
$373$	17.9635	+	17.9635i	0.930116	+	0.930116i	0.997713	−	0.0675964i	$-0.0215330\pi$
$373$	17.9635	+	17.9635i	0.930116	+	0.930116i	−0.0675964	+	0.997713i	$0.521533\pi$
$374$		−	36.1244i		−	1.86795i
$375$		0			0
$376$	−4.73205			−0.244037
$377$	18.2832	+	18.2832i	0.941635	+	0.941635i
$378$	−7.82526	−	7.82526i	−0.402488	−	0.402488i
$379$	22.4950			1.15549			0.577744	−	0.816218i	$-0.303933\pi$
$379$	22.4950			1.15549			0.577744	+	0.816218i	$0.303933\pi$
$380$		0			0
$381$	−14.1962			−0.727291
$382$	7.82526	−	7.82526i	0.400375	−	0.400375i
$383$	1.10245	+	1.10245i	0.0563324	+	0.0563324i	0.734712	−	0.678379i	$-0.237317\pi$
$383$	1.10245	+	1.10245i	0.0563324	+	0.0563324i	−0.678379	+	0.734712i	$0.737317\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$	−15.5885			−0.793432
$387$		0			0
$388$	1.10245	+	1.10245i	0.0559683	+	0.0559683i
$389$	−18.4443			−0.935163			−0.467582	−	0.883950i	$-0.654875\pi$
$389$	−18.4443			−0.935163			−0.467582	+	0.883950i	$0.654875\pi$
$390$		0			0
$391$	34.0788	−	4.54486i	1.72344	−	0.229844i
$392$	1.74238	+	1.74238i	0.0880036	+	0.0880036i
$393$	−17.1464	+	17.1464i	−0.864923	+	0.864923i
$394$		−	6.33975i		−	0.319392i
$395$		0			0
$396$		0			0
$397$	−3.58630	−	3.58630i	−0.179991	−	0.179991i	0.611361	−	0.791352i	$-0.290622\pi$
$397$	−3.58630	−	3.58630i	−0.179991	−	0.179991i	−0.791352	+	0.611361i	$0.790622\pi$
$398$	−9.73475	−	9.73475i	−0.487959	−	0.487959i
$399$		−	18.5885i		−	0.930587i
$400$		0			0
$401$		−	15.1172i		−	0.754919i	−0.926026	−	0.377459i	$-0.876798\pi$
$401$		−	15.1172i		−	0.754919i	0.926026	−	0.377459i	$-0.123202\pi$
$402$	3.56317	−	3.56317i	0.177715	−	0.177715i
$403$	−15.8338	+	15.8338i	−0.788735	+	0.788735i
$404$			17.1244i			0.851969i
$405$		0			0
$406$			11.6373i			0.577547i
$407$	20.7327	+	20.7327i	1.02768	+	1.02768i
$408$	−8.78000	−	8.78000i	−0.434675	−	0.434675i
$409$			5.53590i			0.273733i	0.990590	+	0.136866i	$0.0437031\pi$
$409$			5.53590i			0.273733i	−0.990590	+	0.136866i	$0.956297\pi$
$410$		0			0
$411$			12.4168i			0.612476i
$412$	−3.41547	+	3.41547i	−0.168268	+	0.168268i
$413$	−0.807048	−	0.807048i	−0.0397122	−	0.0397122i
$414$		0			0
$415$		0			0
$416$	−4.73205			−0.232008
$417$	19.5080	+	19.5080i	0.955310	+	0.955310i
$418$	17.9551	−	17.9551i	0.878211	−	0.878211i
$419$	−25.1954			−1.23088			−0.615438	−	0.788186i	$-0.711021\pi$
$419$	−25.1954			−1.23088			−0.615438	+	0.788186i	$0.711021\pi$
$420$		0			0
$421$		−	35.9002i		−	1.74967i	−0.484423	−	0.874834i	$-0.660970\pi$
$421$		−	35.9002i		−	1.74967i	0.484423	−	0.874834i	$-0.339030\pi$
$422$	−0.328169	−	0.328169i	−0.0159750	−	0.0159750i
$423$		0			0
$424$	13.7670			0.668585
$425$		0			0
$426$	−1.85641			−0.0899432
$427$	−5.55532	−	5.55532i	−0.268841	−	0.268841i
$428$	5.06914	+	5.06914i	0.245026	+	0.245026i
$429$	−41.3010			−1.99403
$430$		0			0
$431$		−	23.8452i		−	1.14858i	−0.818651	−	0.574291i	$-0.805278\pi$
$431$		−	23.8452i		−	1.14858i	0.818651	−	0.574291i	$-0.194722\pi$
$432$	−3.67423	−	3.67423i	−0.176777	−	0.176777i
$433$	11.0930	+	11.0930i	0.533097	+	0.533097i	0.921493	−	0.388396i	$-0.126971\pi$
$433$	11.0930	+	11.0930i	0.533097	+	0.533097i	−0.388396	+	0.921493i	$0.626971\pi$
$434$	−10.0782			−0.483767
$435$		0			0
$436$			10.0782i			0.482656i
$437$	19.1973	+	14.6794i	0.918333	+	0.702212i
$438$	−0.984508	+	0.984508i	−0.0470416	+	0.0470416i
$439$			16.9808i			0.810448i	0.914218	+	0.405224i	$0.132806\pi$
$439$			16.9808i			0.810448i	−0.914218	+	0.405224i	$0.867194\pi$
$440$		0			0
$441$		0			0
$442$	23.9874	−	23.9874i	1.14096	−	1.14096i
$443$	4.33057	−	4.33057i	0.205752	−	0.205752i	−0.596707	−	0.802459i	$-0.703525\pi$
$443$	4.33057	−	4.33057i	0.205752	−	0.205752i	0.802459	+	0.596707i	$0.203525\pi$
$444$	10.0782			0.478288
$445$		0			0
$446$	4.39230			0.207982
$447$	−16.8611	+	16.8611i	−0.797502	+	0.797502i
$448$	−1.50597	−	1.50597i	−0.0711505	−	0.0711505i
$449$		−	8.85641i		−	0.417960i	−0.977920	−	0.208980i	$-0.932986\pi$
$449$		−	8.85641i		−	0.417960i	0.977920	−	0.208980i	$-0.0670143\pi$
$450$		0			0
$451$		−	60.1071i		−	2.83033i
$452$	8.08108	−	8.08108i	0.380102	−	0.380102i
$453$	2.68973	−	2.68973i	0.126374	−	0.126374i
$454$		0			0
$455$		0			0
$456$		−	8.72794i		−	0.408723i
$457$	−5.36454	+	5.36454i	−0.250942	+	0.250942i	−0.821357	−	0.570415i	$-0.806783\pi$
$457$	−5.36454	+	5.36454i	−0.250942	+	0.250942i	0.570415	+	0.821357i	$0.306783\pi$
$458$	−4.51791	−	4.51791i	−0.211108	−	0.211108i
$459$	37.2504			1.73870
$460$		0			0
$461$	0.392305			0.0182715			0.00913573	−	0.999958i	$-0.497092\pi$
$461$	0.392305			0.0182715			0.00913573	+	0.999958i	$0.497092\pi$
$462$	−13.1440	−	13.1440i	−0.611515	−	0.611515i
$463$	7.76457	−	7.76457i	0.360850	−	0.360850i	−0.503276	−	0.864126i	$-0.667872\pi$
$463$	7.76457	−	7.76457i	0.360850	−	0.360850i	0.864126	+	0.503276i	$0.167872\pi$
$464$			5.46410i			0.253665i
$465$		0			0
$466$	−1.85641			−0.0859964
$467$	23.2885	−	23.2885i	1.07766	−	1.07766i	0.0809442	−	0.996719i	$-0.474206\pi$
$467$	23.2885	−	23.2885i	1.07766	−	1.07766i	0.996719	−	0.0809442i	$-0.0257936\pi$
$468$		0			0
$469$			6.19615i			0.286112i
$470$		0			0
$471$		−	22.8567i		−	1.05318i
$472$	−0.378937	−	0.378937i	−0.0174420	−	0.0174420i
$473$	5.55532	−	5.55532i	0.255434	−	0.255434i
$474$	−4.67729			−0.214835
$475$		0			0
$476$	15.2679			0.699805
$477$		0			0
$478$	−4.76028	+	4.76028i	−0.217730	+	0.217730i
$479$	1.71201			0.0782236			0.0391118	−	0.999235i	$-0.487547\pi$
$479$	1.71201			0.0782236			0.0391118	+	0.999235i	$0.487547\pi$
$480$		0			0
$481$			27.5340i			1.25544i
$482$	8.78000	−	8.78000i	0.399918	−	0.399918i
$483$	10.7461	−	14.0534i	0.488964	−	0.639453i
$484$		−	14.3923i		−	0.654196i
$485$		0			0
$486$		0			0
$487$	−19.4201	−	19.4201i	−0.880007	−	0.880007i	0.113528	−	0.993535i	$-0.463785\pi$
$487$	−19.4201	−	19.4201i	−0.880007	−	0.880007i	−0.993535	+	0.113528i	$0.963785\pi$
$488$	−2.60842	−	2.60842i	−0.118078	−	0.118078i
$489$		−	28.1769i		−	1.27420i
$490$		0			0
$491$	4.53590			0.204702			0.102351	−	0.994748i	$-0.467363\pi$
$491$	4.53590			0.204702			0.102351	+	0.994748i	$0.467363\pi$
$492$	−14.6090	−	14.6090i	−0.658625	−	0.658625i
$493$	−27.6983	−	27.6983i	−1.24747	−	1.24747i
$494$	23.8452			1.07285
$495$		0			0
$496$	−4.73205			−0.212475
$497$	1.61410	−	1.61410i	0.0724021	−	0.0724021i
$498$	19.7253	+	19.7253i	0.883913	+	0.883913i
$499$			22.0000i			0.984855i	0.870353	+	0.492428i	$0.163890\pi$
$499$			22.0000i			0.984855i	−0.870353	+	0.492428i	$0.836110\pi$
$500$		0			0
$501$	−16.9808			−0.758645
$502$	1.65367	−	1.65367i	0.0738070	−	0.0738070i
$503$	−5.21684	−	5.21684i	−0.232607	−	0.232607i	0.581173	−	0.813780i	$-0.302594\pi$
$503$	−5.21684	−	5.21684i	−0.232607	−	0.232607i	−0.813780	+	0.581173i	$0.802594\pi$
$504$		0			0
$505$		0			0
$506$	23.9545	−	3.19465i	1.06491	−	0.142019i
$507$	−11.5032	−	11.5032i	−0.510874	−	0.510874i
$508$	5.79555	−	5.79555i	0.257136	−	0.257136i
$509$		−	22.1962i		−	0.983827i	−0.870644	−	0.491914i	$-0.836298\pi$
$509$		−	22.1962i		−	0.983827i	0.870644	−	0.491914i	$-0.163702\pi$
$510$		0			0
$511$		−	1.71201i		−	0.0757347i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	18.5148	+	18.5148i	0.817446	+	0.817446i
$514$			27.4641i			1.21139i
$515$		0			0
$516$		−	2.70043i		−	0.118880i
$517$	16.8611	−	16.8611i	0.741550	−	0.741550i
$518$	−8.76268	+	8.76268i	−0.385010	+	0.385010i
$519$			32.7846i			1.43908i
$520$		0			0
$521$			20.5181i			0.898914i	0.893302	+	0.449457i	$0.148383\pi$
$521$			20.5181i			0.898914i	−0.893302	+	0.449457i	$0.851617\pi$
$522$		0			0
$523$	−10.5814	−	10.5814i	−0.462691	−	0.462691i	0.436845	−	0.899537i	$-0.356096\pi$
$523$	−10.5814	−	10.5814i	−0.462691	−	0.462691i	−0.899537	+	0.436845i	$0.856096\pi$
$524$		−	14.0000i		−	0.611593i
$525$		0			0
$526$		−	0.988427i		−	0.0430975i
$527$	23.9874	−	23.9874i	1.04491	−	1.04491i
$528$	−6.17158	−	6.17158i	−0.268584	−	0.268584i
$529$	6.02751	+	22.1962i	0.262065	+	0.965050i
$530$		0			0
$531$		0			0
$532$	7.58871	+	7.58871i	0.329012	+	0.329012i
$533$	39.9125	−	39.9125i	1.72880	−	1.72880i
$534$	21.5065			0.930678
$535$		0			0
$536$			2.90931i			0.125663i
$537$	1.22474	+	1.22474i	0.0528516	+	0.0528516i
$538$	15.3161	−	15.3161i	0.660324	−	0.660324i
$539$	−12.4168			−0.534829
$540$		0			0
$541$	−16.3923			−0.704760			−0.352380	−	0.935857i	$-0.614628\pi$
$541$	−16.3923			−0.704760			−0.352380	+	0.935857i	$0.614628\pi$
$542$	16.1112	+	16.1112i	0.692033	+	0.692033i
$543$	21.3790	+	21.3790i	0.917461	+	0.917461i
$544$	7.16884			0.307362
$545$		0			0
$546$		−	17.4559i		−	0.747043i
$547$	9.88589	+	9.88589i	0.422690	+	0.422690i	0.886129	−	0.463439i	$-0.153385\pi$
$547$	9.88589	+	9.88589i	0.422690	+	0.422690i	−0.463439	+	0.886129i	$0.653385\pi$
$548$	−5.06914	−	5.06914i	−0.216543	−	0.216543i
$549$		0			0
$550$		0			0
$551$		−	27.5340i		−	1.17299i
$552$	5.04567	−	6.59858i	0.214758	−	0.280854i
$553$	4.06678	−	4.06678i	0.172937	−	0.172937i
$554$			25.8564i			1.09853i
$555$		0			0
$556$	−15.9282			−0.675506
$557$	−21.2709	+	21.2709i	−0.901276	+	0.901276i	−0.995547	−	0.0942708i	$-0.969948\pi$
$557$	−21.2709	+	21.2709i	−0.901276	+	0.901276i	0.0942708	+	0.995547i	$0.469948\pi$
$558$		0			0
$559$	7.37772			0.312044
$560$		0			0
$561$	62.5692			2.64167
$562$	1.90949	−	1.90949i	0.0805472	−	0.0805472i
$563$	−20.2765	−	20.2765i	−0.854555	−	0.854555i	0.136136	−	0.990690i	$-0.456532\pi$
$563$	−20.2765	−	20.2765i	−0.854555	−	0.854555i	−0.990690	+	0.136136i	$0.956532\pi$
$564$		−	8.19615i		−	0.345120i
$565$		0			0
$566$			32.0024i			1.34516i
$567$	13.5537	−	13.5537i	0.569204	−	0.569204i
$568$	0.757875	−	0.757875i	0.0317997	−	0.0317997i
$569$	17.0941			0.716621			0.358311	−	0.933602i	$-0.383353\pi$
$569$	17.0941			0.716621			0.358311	+	0.933602i	$0.383353\pi$
$570$		0			0
$571$		−	22.8567i		−	0.956525i	−0.878217	−	0.478262i	$-0.841267\pi$
$571$		−	22.8567i		−	0.956525i	0.878217	−	0.478262i	$-0.158733\pi$
$572$	16.8611	−	16.8611i	0.704997	−	0.704997i
$573$	13.5537	+	13.5537i	0.566216	+	0.566216i
$574$	25.4043			1.06035
$575$		0			0
$576$		0			0
$577$	−9.05369	−	9.05369i	−0.376910	−	0.376910i	0.493076	−	0.869986i	$-0.335872\pi$
$577$	−9.05369	−	9.05369i	−0.376910	−	0.376910i	−0.869986	+	0.493076i	$0.835872\pi$
$578$	−24.3190	+	24.3190i	−1.01154	+	1.01154i
$579$		−	27.0000i		−	1.12208i
$580$		0			0
$581$	−34.3013			−1.42306
$582$	−1.90949	+	1.90949i	−0.0791511	+	0.0791511i
$583$	−49.0542	+	49.0542i	−2.03162	+	2.03162i
$584$		−	0.803848i		−	0.0332634i
$585$		0			0
$586$		−	12.6257i		−	0.521562i
$587$	−20.8207	−	20.8207i	−0.859361	−	0.859361i	0.131902	−	0.991263i	$-0.457892\pi$
$587$	−20.8207	−	20.8207i	−0.859361	−	0.859361i	−0.991263	+	0.131902i	$0.957892\pi$
$588$	−3.01790	+	3.01790i	−0.124456	+	0.124456i
$589$	23.8452			0.982523
$590$		0			0
$591$	10.9808			0.451688
$592$	−4.11439	+	4.11439i	−0.169100	+	0.169100i
$593$	−19.5080	+	19.5080i	−0.801097	+	0.801097i	−0.983267	−	0.182170i	$-0.941688\pi$
$593$	−19.5080	+	19.5080i	−0.801097	+	0.801097i	0.182170	+	0.983267i	$0.441688\pi$
$594$	26.1838			1.07433
$595$		0			0
$596$		−	13.7670i		−	0.563919i
$597$	16.8611	−	16.8611i	0.690078	−	0.690078i
$598$	18.0277	+	13.7850i	0.737206	+	0.563711i
$599$			6.19615i			0.253168i	0.991956	+	0.126584i	$0.0404013\pi$
$599$			6.19615i			0.253168i	−0.991956	+	0.126584i	$0.959599\pi$
$600$		0			0
$601$	−33.3923			−1.36210			−0.681050	−	0.732237i	$-0.738476\pi$
$601$	−33.3923			−1.36210			−0.681050	+	0.732237i	$0.738476\pi$
$602$	2.34795	+	2.34795i	0.0956955	+	0.0956955i
$603$		0			0
$604$			2.19615i			0.0893602i
$605$		0			0
$606$	−29.6603			−1.20487
$607$	18.0430	+	18.0430i	0.732343	+	0.732343i	0.971083	−	0.238740i	$-0.0767345\pi$
$607$	18.0430	+	18.0430i	0.732343	+	0.732343i	−0.238740	+	0.971083i	$0.576735\pi$
$608$	3.56317	+	3.56317i	0.144505	+	0.144505i
$609$	−20.1563			−0.816775
$610$		0			0
$611$	22.3923			0.905896
$612$		0			0
$613$	−6.72281	−	6.72281i	−0.271532	−	0.271532i	0.558185	−	0.829717i	$-0.311498\pi$
$613$	−6.72281	−	6.72281i	−0.271532	−	0.271532i	−0.829717	+	0.558185i	$0.811498\pi$
$614$		−	5.87564i		−	0.237122i
$615$		0			0
$616$	10.7321			0.432407
$617$	−1.39785	+	1.39785i	−0.0562752	+	0.0562752i	−0.734684	−	0.678409i	$-0.762670\pi$
$617$	−1.39785	+	1.39785i	−0.0562752	+	0.0562752i	0.678409	+	0.734684i	$0.262670\pi$
$618$	−5.91576	−	5.91576i	−0.237967	−	0.237967i
$619$	−43.0131			−1.72884			−0.864420	−	0.502770i	$-0.832314\pi$
$619$	−43.0131			−1.72884			−0.864420	+	0.502770i	$0.832314\pi$
$620$		0			0
$621$	3.29423	+	24.7012i	0.132193	+	0.991224i
$622$	21.7680	+	21.7680i	0.872818	+	0.872818i
$623$	−18.6993	+	18.6993i	−0.749173	+	0.749173i
$624$		−	8.19615i		−	0.328109i
$625$		0			0
$626$		−	8.93682i		−	0.357187i
$627$	31.0991	+	31.0991i	1.24198	+	1.24198i
$628$	9.33123	+	9.33123i	0.372356	+	0.372356i
$629$		−	41.7128i		−	1.66320i
$630$		0			0
$631$		−	39.5890i		−	1.57601i	−0.615666	−	0.788007i	$-0.711113\pi$
$631$		−	39.5890i		−	1.57601i	0.615666	−	0.788007i	$-0.288887\pi$
$632$	1.90949	−	1.90949i	0.0759556	−	0.0759556i
$633$	0.568406	−	0.568406i	0.0225921	−	0.0225921i
$634$		−	18.2487i		−	0.724749i
$635$		0			0
$636$			23.8452i			0.945523i
$637$	−8.24504	−	8.24504i	−0.326681	−	0.326681i
$638$	−19.4695	−	19.4695i	−0.770805	−	0.770805i
$639$		0			0
$640$		0			0
$641$		−	47.6903i		−	1.88366i	−0.336096	−	0.941828i	$-0.609107\pi$
$641$		−	47.6903i		−	1.88366i	0.336096	−	0.941828i	$-0.390893\pi$
$642$	−8.78000	+	8.78000i	−0.346519	+	0.346519i
$643$	−12.6386	−	12.6386i	−0.498417	−	0.498417i	0.412528	−	0.910945i	$-0.364646\pi$
$643$	−12.6386	−	12.6386i	−0.498417	−	0.498417i	−0.910945	+	0.412528i	$0.864646\pi$
$644$	1.35022	+	10.1244i	0.0532060	+	0.398956i
$645$		0			0
$646$	−36.1244			−1.42129
$647$	−1.79315	−	1.79315i	−0.0704960	−	0.0704960i	0.670980	−	0.741476i	$-0.265874\pi$
$647$	−1.79315	−	1.79315i	−0.0704960	−	0.0704960i	−0.741476	+	0.670980i	$0.765874\pi$
$648$	6.36396	−	6.36396i	0.250000	−	0.250000i
$649$	2.70043			0.106001
$650$		0			0
$651$		−	17.4559i		−	0.684150i
$652$	11.5032	+	11.5032i	0.450499	+	0.450499i
$653$	24.3190	−	24.3190i	0.951677	−	0.951677i	−0.0472078	−	0.998885i	$-0.515032\pi$
$653$	24.3190	−	24.3190i	0.951677	−	0.951677i	0.998885	+	0.0472078i	$0.0150323\pi$
$654$	−17.4559			−0.682579
$655$		0			0
$656$	11.9282			0.465718
$657$		0			0
$658$	7.12633	+	7.12633i	0.277813	+	0.277813i
$659$	37.2504			1.45107			0.725535	−	0.688186i	$-0.241592\pi$
$659$	37.2504			1.45107			0.725535	+	0.688186i	$0.241592\pi$
$660$		0			0
$661$			14.7554i			0.573920i	0.957943	+	0.286960i	$0.0926447\pi$
$661$			14.7554i			0.573920i	−0.957943	+	0.286960i	$0.907355\pi$
$662$	−13.9898	−	13.9898i	−0.543730	−	0.543730i
$663$	41.5474	+	41.5474i	1.61357	+	1.61357i
$664$	−16.1057			−0.625021
$665$		0			0
$666$		0			0
$667$	15.9176	−	20.8165i	0.616331	−	0.806020i
$668$	6.93237	−	6.93237i	0.268221	−	0.268221i
$669$			7.60770i			0.294130i
$670$		0			0
$671$	18.5885			0.717599
$672$	2.60842	−	2.60842i	0.100622	−	0.100622i
$673$	−16.3142	+	16.3142i	−0.628867	+	0.628867i	−0.947783	−	0.318916i	$-0.896681\pi$
$673$	−16.3142	+	16.3142i	−0.628867	+	0.628867i	0.318916	+	0.947783i	$0.396681\pi$
$674$	19.9474			0.768346
$675$		0			0
$676$	9.39230			0.361242
$677$	22.0779	−	22.0779i	0.848523	−	0.848523i	−0.141426	−	0.989949i	$-0.545169\pi$
$677$	22.0779	−	22.0779i	0.848523	−	0.848523i	0.989949	+	0.141426i	$0.0451686\pi$
$678$	13.9968	+	13.9968i	0.537545	+	0.537545i
$679$		−	3.32051i		−	0.127429i
$680$		0			0
$681$		0			0
$682$	16.8611	−	16.8611i	0.645644	−	0.645644i
$683$	−1.88108	+	1.88108i	−0.0719777	+	0.0719777i	−0.742179	−	0.670202i	$-0.766208\pi$
$683$	−1.88108	+	1.88108i	−0.0719777	+	0.0719777i	0.670202	+	0.742179i	$0.266208\pi$
$684$		0			0
$685$		0			0
$686$		−	20.1563i		−	0.769572i
$687$	7.82526	−	7.82526i	0.298552	−	0.298552i
$688$	1.10245	+	1.10245i	0.0420304	+	0.0420304i
$689$	−65.1462			−2.48187
$690$		0			0
$691$	22.1769			0.843650			0.421825	−	0.906677i	$-0.361390\pi$
$691$	22.1769			0.843650			0.421825	+	0.906677i	$0.361390\pi$
$692$	−13.3843	−	13.3843i	−0.508793	−	0.508793i
$693$		0			0
$694$			36.1244i			1.37126i
$695$		0			0
$696$	−9.46410			−0.358736
$697$	−60.4657	+	60.4657i	−2.29030	+	2.29030i
$698$	7.62587	−	7.62587i	0.288643	−	0.288643i
$699$		−	3.21539i		−	0.121617i
$700$		0			0
$701$		−	1.97685i		−	0.0746648i	−0.999303	−	0.0373324i	$-0.988114\pi$
$701$		−	1.97685i		−	0.0746648i	0.999303	−	0.0373324i	$-0.0118860\pi$
$702$	17.3867	+	17.3867i	0.656217	+	0.656217i
$703$	20.7327	−	20.7327i	0.781950	−	0.781950i
$704$	5.03908			0.189917
$705$		0			0
$706$	20.5359			0.772879
$707$	25.7888	−	25.7888i	0.969887	−	0.969887i
$708$	0.656339	−	0.656339i	0.0246667	−	0.0246667i
$709$	40.3126			1.51397			0.756986	−	0.653431i	$-0.226671\pi$
$709$	40.3126			1.51397			0.756986	+	0.653431i	$0.226671\pi$
$710$		0			0
$711$		0			0
$712$	−8.78000	+	8.78000i	−0.329045	+	0.329045i
$713$	18.0277	+	13.7850i	0.675141	+	0.516253i
$714$			26.4449i			0.989674i
$715$		0			0
$716$	−1.00000			−0.0373718
$717$	−8.24504	−	8.24504i	−0.307917	−	0.307917i
$718$	7.82526	+	7.82526i	0.292036	+	0.292036i
$719$		−	12.7321i		−	0.474825i	−0.971409	−	0.237413i	$-0.923701\pi$
$719$		−	12.7321i		−	0.474825i	0.971409	−	0.237413i	$-0.0762994\pi$
$720$		0			0
$721$	10.2872			0.383115
$722$	−4.52004	−	4.52004i	−0.168219	−	0.168219i
$723$	15.2074	+	15.2074i	0.565570	+	0.565570i
$724$	−17.4559			−0.648743
$725$		0			0
$726$	24.9282			0.925172
$727$	−0.807048	+	0.807048i	−0.0299317	+	0.0299317i	−0.721914	−	0.691983i	$-0.756738\pi$
$727$	−0.807048	+	0.807048i	−0.0299317	+	0.0299317i	0.691983	+	0.721914i	$0.256738\pi$
$728$	7.12633	+	7.12633i	0.264119	+	0.264119i
$729$			27.0000i			1.00000i
$730$		0			0
$731$	−11.1769			−0.413393
$732$	4.51791	−	4.51791i	0.166987	−	0.166987i
$733$	−13.8491	−	13.8491i	−0.511530	−	0.511530i	0.403465	−	0.914995i	$-0.367806\pi$
$733$	−13.8491	−	13.8491i	−0.511530	−	0.511530i	−0.914995	+	0.403465i	$0.867806\pi$
$734$	22.7038			0.838014
$735$		0			0
$736$	0.633975	+	4.75374i	0.0233686	+	0.175225i
$737$	−10.3664	−	10.3664i	−0.381850	−	0.381850i
$738$		0			0
$739$		−	19.8564i		−	0.730430i	−0.930923	−	0.365215i	$-0.880996\pi$
$739$		−	19.8564i		−	0.730430i	0.930923	−	0.365215i	$-0.119004\pi$
$740$		0			0
$741$			41.3010i			1.51723i
$742$	−20.7327	−	20.7327i	−0.761122	−	0.761122i
$743$	−19.1741	−	19.1741i	−0.703430	−	0.703430i	0.261716	−	0.965145i	$-0.415712\pi$
$743$	−19.1741	−	19.1741i	−0.703430	−	0.703430i	−0.965145	+	0.261716i	$0.915712\pi$
$744$		−	8.19615i		−	0.300486i
$745$		0			0
$746$		−	25.4043i		−	0.930116i
$747$		0			0
$748$	−25.5438	+	25.5438i	−0.933973	+	0.933973i
$749$		−	15.2679i		−	0.557879i
$750$		0			0
$751$		−	32.9349i		−	1.20181i	−0.799320	−	0.600906i	$-0.794807\pi$
$751$		−	32.9349i		−	1.20181i	0.799320	−	0.600906i	$-0.205193\pi$
$752$	3.34607	+	3.34607i	0.122018	+	0.122018i
$753$	2.86424	+	2.86424i	0.104379	+	0.104379i
$754$		−	25.8564i		−	0.941635i
$755$		0			0
$756$			11.0666i			0.402488i
$757$	23.8793	−	23.8793i	0.867908	−	0.867908i	−0.124333	−	0.992241i	$-0.539679\pi$
$757$	23.8793	−	23.8793i	0.867908	−	0.867908i	0.992241	+	0.124333i	$0.0396791\pi$
$758$	−15.9063	−	15.9063i	−0.577744	−	0.577744i
$759$	5.53329	+	41.4904i	0.200846	+	1.50601i
$760$		0			0
$761$	−2.85641			−0.103545			−0.0517723	−	0.998659i	$-0.516487\pi$
$761$	−2.85641			−0.103545			−0.0517723	+	0.998659i	$0.516487\pi$
$762$	10.0382	+	10.0382i	0.363645	+	0.363645i
$763$	15.1774	−	15.1774i	0.549459	−	0.549459i
$764$	−11.0666			−0.400375
$765$		0			0
$766$		−	1.55910i		−	0.0563324i
$767$	1.79315	+	1.79315i	0.0647469	+	0.0647469i
$768$	1.22474	−	1.22474i	0.0441942	−	0.0441942i
$769$	−7.73951			−0.279094			−0.139547	−	0.990215i	$-0.544565\pi$
$769$	−7.73951			−0.279094			−0.139547	+	0.990215i	$0.544565\pi$
$770$		0			0
$771$	−47.5692			−1.71316
$772$	11.0227	+	11.0227i	0.396716	+	0.396716i
$773$	−20.2765	−	20.2765i	−0.729297	−	0.729297i	0.241183	−	0.970480i	$-0.422465\pi$
$773$	−20.2765	−	20.2765i	−0.729297	−	0.729297i	−0.970480	+	0.241183i	$0.922465\pi$
$774$		0			0
$775$		0			0
$776$		−	1.55910i		−	0.0559683i
$777$	−15.1774	−	15.1774i	−0.544487	−	0.544487i
$778$	13.0421	+	13.0421i	0.467582	+	0.467582i
$779$	−60.1071			−2.15356
$780$		0			0
$781$			5.40087i			0.193258i
$782$	−27.3111	−	20.8837i	−0.976642	−	0.746799i
$783$	20.0764	−	20.0764i	0.717472	−	0.717472i
$784$		−	2.46410i		−	0.0880036i
$785$		0			0
$786$	24.2487			0.864923
$787$	−3.01194	+	3.01194i	−0.107364	+	0.107364i	−0.758748	−	0.651384i	$-0.774189\pi$
$787$	−3.01194	+	3.01194i	−0.107364	+	0.107364i	0.651384	+	0.758748i	$0.274189\pi$
$788$	−4.48288	+	4.48288i	−0.159696	+	0.159696i
$789$	1.71201			0.0609490
$790$		0			0
$791$	−24.3397			−0.865422
$792$		0			0
$793$	12.3432	+	12.3432i	0.438319	+	0.438319i
$794$			5.07180i			0.179991i
$795$		0			0
$796$			13.7670i			0.487959i
$797$	1.10245	−	1.10245i	0.0390507	−	0.0390507i	−0.687312	−	0.726362i	$-0.741209\pi$
$797$	1.10245	−	1.10245i	0.0390507	−	0.0390507i	0.726362	+	0.687312i	$0.241209\pi$
$798$	−13.1440	+	13.1440i	−0.465293	+	0.465293i
$799$	−33.9233			−1.20012
$800$		0			0
$801$		0			0
$802$	−10.6895	+	10.6895i	−0.377459	+	0.377459i
$803$	2.86424	+	2.86424i	0.101077	+	0.101077i
$804$	−5.03908			−0.177715
$805$		0			0
$806$	22.3923			0.788735
$807$	26.5283	+	26.5283i	0.933840	+	0.933840i
$808$	12.1087	−	12.1087i	0.425984	−	0.425984i
$809$		−	2.14359i		−	0.0753647i	−0.999290	−	0.0376824i	$-0.988002\pi$
$809$		−	2.14359i		−	0.0753647i	0.999290	−	0.0376824i	$-0.0119975\pi$
$810$		0			0
$811$	−54.7846			−1.92375			−0.961874	−	0.273493i	$-0.911821\pi$
$811$	−54.7846			−1.92375			−0.961874	+	0.273493i	$0.911821\pi$
$812$	8.22878	−	8.22878i	0.288774	−	0.288774i
$813$	−27.9053	+	27.9053i	−0.978683	+	0.978683i
$814$		−	29.3205i		−	1.02768i
$815$		0			0
$816$			12.4168i			0.434675i
$817$	−5.55532	−	5.55532i	−0.194356	−	0.194356i
$818$	3.91447	−	3.91447i	0.136866	−	0.136866i
$819$		0			0
$820$		0			0
$821$	34.5885			1.20715			0.603573	−	0.797308i	$-0.293743\pi$
$821$	34.5885			1.20715			0.603573	+	0.797308i	$0.293743\pi$
$822$	8.78000	−	8.78000i	0.306238	−	0.306238i
$823$	31.4273	−	31.4273i	1.09549	−	1.09549i	0.100554	−	0.994932i	$-0.467938\pi$
$823$	31.4273	−	31.4273i	1.09549	−	1.09549i	0.994932	−	0.100554i	$-0.0320615\pi$
$824$	4.83020			0.168268
$825$		0			0
$826$			1.14134i			0.0397122i
$827$	28.9484	−	28.9484i	1.00664	−	1.00664i	0.00665765	−	0.999978i	$-0.497881\pi$
$827$	28.9484	−	28.9484i	1.00664	−	1.00664i	0.999978	−	0.00665765i	$-0.00211921\pi$
$828$		0			0
$829$			34.6410i			1.20313i	0.798823	+	0.601566i	$0.205456\pi$
$829$			34.6410i			1.20313i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	−44.7846			−1.55356
$832$	3.34607	+	3.34607i	0.116004	+	0.116004i
$833$	12.4909	+	12.4909i	0.432783	+	0.432783i
$834$		−	27.5885i		−	0.955310i
$835$		0			0
$836$	−25.3923			−0.878211
$837$	17.3867	+	17.3867i	0.600971	+	0.600971i
$838$	17.8158	+	17.8158i	0.615438	+	0.615438i
$839$	−8.36615			−0.288832			−0.144416	−	0.989517i	$-0.546130\pi$
$839$	−8.36615			−0.288832			−0.144416	+	0.989517i	$0.546130\pi$
$840$		0			0
$841$	−0.856406			−0.0295313
$842$	−25.3853	+	25.3853i	−0.874834	+	0.874834i
$843$	3.30734	+	3.30734i	0.113911	+	0.113911i
$844$			0.464102i			0.0159750i
$845$		0			0
$846$		0			0
$847$	−21.6744	+	21.6744i	−0.744741	+	0.744741i
$848$	−9.73475	−	9.73475i	−0.334293	−	0.334293i
$849$	−55.4299			−1.90235
$850$		0			0
$851$	27.6603	−	3.68886i	0.948181	−	0.126453i
$852$	1.31268	+	1.31268i	0.0449716	+	0.0449716i
$853$	12.9682	−	12.9682i	0.444021	−	0.444021i	−0.449340	−	0.893361i	$-0.648341\pi$
$853$	12.9682	−	12.9682i	0.444021	−	0.444021i	0.893361	+	0.449340i	$0.148341\pi$
$854$			7.85641i			0.268841i
$855$		0			0
$856$		−	7.16884i		−	0.245026i
$857$	14.6090	+	14.6090i	0.499034	+	0.499034i	0.911137	−	0.412103i	$-0.135206\pi$
$857$	14.6090	+	14.6090i	0.499034	+	0.499034i	−0.412103	+	0.911137i	$0.635206\pi$
$858$	29.2043	+	29.2043i	0.997017	+	0.997017i
$859$		−	11.3923i		−	0.388700i	−0.980932	−	0.194350i	$-0.937740\pi$
$859$		−	11.3923i		−	0.388700i	0.980932	−	0.194350i	$-0.0622598\pi$
$860$		0			0
$861$			44.0015i			1.49957i
$862$	−16.8611	+	16.8611i	−0.574291	+	0.574291i
$863$	−33.9411	+	33.9411i	−1.15537	+	1.15537i	−0.169910	+	0.985460i	$0.554348\pi$
$863$	−33.9411	+	33.9411i	−1.15537	+	1.15537i	−0.985460	+	0.169910i	$0.945652\pi$
$864$			5.19615i			0.176777i
$865$		0			0
$866$		−	15.6879i		−	0.533097i
$867$	−42.1218	−	42.1218i	−1.43053	−	1.43053i
$868$	7.12633	+	7.12633i	0.241883	+	0.241883i
$869$			13.6077i			0.461609i
$870$		0			0
$871$		−	13.7670i		−	0.466478i
$872$	7.12633	−	7.12633i	0.241328	−	0.241328i
$873$		0			0
$874$	−3.19465	−	23.9545i	−0.108061	−	0.810272i
$875$		0			0
$876$	1.39230			0.0470416
$877$	10.0382	+	10.0382i	0.338966	+	0.338966i	0.855978	−	0.517012i	$-0.172956\pi$
$877$	10.0382	+	10.0382i	0.338966	+	0.338966i	−0.517012	+	0.855978i	$0.672956\pi$
$878$	12.0072	−	12.0072i	0.405224	−	0.405224i
$879$	21.8683			0.737600
$880$		0			0
$881$			22.1332i			0.745685i	0.927895	+	0.372843i	$0.121617\pi$
$881$			22.1332i			0.745685i	−0.927895	+	0.372843i	$0.878383\pi$
$882$		0			0
$883$	−23.9265	+	23.9265i	−0.805191	+	0.805191i	−0.983902	−	0.178711i	$-0.942807\pi$
$883$	−23.9265	+	23.9265i	−0.805191	+	0.805191i	0.178711	+	0.983902i	$0.442807\pi$
$884$	−33.9233			−1.14096
$885$		0			0
$886$	−6.12436			−0.205752
$887$	−11.1106	−	11.1106i	−0.373059	−	0.373059i	0.495531	−	0.868590i	$-0.334973\pi$
$887$	−11.1106	−	11.1106i	−0.373059	−	0.373059i	−0.868590	+	0.495531i	$0.834973\pi$
$888$	−7.12633	−	7.12633i	−0.239144	−	0.239144i
$889$	−17.4559			−0.585451
$890$		0			0
$891$			45.3517i			1.51934i
$892$	−3.10583	−	3.10583i	−0.103991	−	0.103991i
$893$	−16.8611	−	16.8611i	−0.564235	−	0.564235i
$894$	23.8452			0.797502
$895$		0			0
$896$			2.12976i			0.0711505i
$897$	−23.8763	+	31.2248i	−0.797208	+	1.04257i
$898$	−6.26243	+	6.26243i	−0.208980	+	0.208980i
$899$		−	25.8564i		−	0.862359i
$900$		0			0
$901$	98.6936			3.28796
$902$	−42.5022	+	42.5022i	−1.41517	+	1.41517i
$903$	−4.06678	+	4.06678i	−0.135334	+	0.135334i
$904$	−11.4284			−0.380102
$905$		0			0
$906$	−3.80385			−0.126374
$907$	−39.7461	+	39.7461i	−1.31975	+	1.31975i	−0.405771	+	0.913975i	$0.632997\pi$
$907$	−39.7461	+	39.7461i	−1.31975	+	1.31975i	−0.913975	+	0.405771i	$0.867003\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			33.9233i			1.12393i	0.827161	+	0.561965i	$0.189954\pi$
$911$			33.9233i			1.12393i	−0.827161	+	0.561965i	$0.810046\pi$
$912$	−6.17158	+	6.17158i	−0.204362	+	0.204362i
$913$	57.3871	−	57.3871i	1.89924	−	1.89924i
$914$	7.58660			0.250942
$915$		0			0
$916$			6.38929i			0.211108i
$917$	−21.0836	+	21.0836i	−0.696242	+	0.696242i
$918$	−26.3400	−	26.3400i	−0.869350	−	0.869350i
$919$	−9.08973			−0.299842			−0.149921	−	0.988698i	$-0.547902\pi$
$919$	−9.08973			−0.299842			−0.149921	+	0.988698i	$0.547902\pi$
$920$		0			0
$921$	10.1769			0.335341
$922$	−0.277401	−	0.277401i	−0.00913573	−	0.00913573i
$923$	−3.58630	+	3.58630i	−0.118045	+	0.118045i
$924$			18.5885i			0.611515i
$925$		0			0
$926$	−10.9808			−0.360850
$927$		0			0
$928$	3.86370	−	3.86370i	0.126832	−	0.126832i
$929$			48.1051i			1.57828i	0.614215	+	0.789139i	$0.289473\pi$
$929$			48.1051i			1.57828i	−0.614215	+	0.789139i	$0.710527\pi$
$930$		0			0
$931$			12.4168i			0.406944i
$932$	1.31268	+	1.31268i	0.0429982	+	0.0429982i
$933$	−37.7033	+	37.7033i	−1.23435	+	1.23435i
$934$	−32.9349			−1.07766
$935$		0			0
$936$		0			0
$937$	0.659348	−	0.659348i	0.0215399	−	0.0215399i	−0.696255	−	0.717795i	$-0.745152\pi$
$937$	0.659348	−	0.659348i	0.0215399	−	0.0215399i	0.717795	+	0.696255i	$0.245152\pi$
$938$	4.38134	−	4.38134i	0.143056	−	0.143056i
$939$	15.4790			0.505139
$940$		0			0
$941$			12.7786i			0.416570i	0.978068	+	0.208285i	$0.0667882\pi$
$941$			12.7786i			0.416570i	−0.978068	+	0.208285i	$0.933212\pi$
$942$	−16.1622	+	16.1622i	−0.526592	+	0.526592i
$943$	−45.4428	−	34.7482i	−1.47982	−	1.13156i
$944$			0.535898i			0.0174420i
$945$		0			0
$946$	−7.85641			−0.255434
$947$	6.69213	+	6.69213i	0.217465	+	0.217465i	0.807429	−	0.589964i	$-0.200858\pi$
$947$	6.69213	+	6.69213i	0.217465	+	0.217465i	−0.589964	+	0.807429i	$0.700858\pi$
$948$	3.30734	+	3.30734i	0.107417	+	0.107417i
$949$			3.80385i			0.123478i
$950$		0			0
$951$	31.6077			1.02495
$952$	−10.7961	−	10.7961i	−0.349903	−	0.349903i
$953$	−6.17158	−	6.17158i	−0.199917	−	0.199917i	0.600047	−	0.799965i	$-0.295148\pi$
$953$	−6.17158	−	6.17158i	−0.199917	−	0.199917i	−0.799965	+	0.600047i	$0.795148\pi$
$954$		0			0
$955$		0			0
$956$	6.73205			0.217730
$957$	33.7222	−	33.7222i	1.09008	−	1.09008i
$958$	−1.21057	−	1.21057i	−0.0391118	−	0.0391118i
$959$			15.2679i			0.493028i
$960$		0			0
$961$	−8.60770			−0.277668
$962$	19.4695	−	19.4695i	0.627722	−	0.627722i
$963$		0			0
$964$	−12.4168			−0.399918
$965$		0			0
$966$	−17.5359	+	2.33864i	−0.564208	+	0.0752446i
$967$	−14.6969	−	14.6969i	−0.472622	−	0.472622i	0.430140	−	0.902762i	$-0.358464\pi$
$967$	−14.6969	−	14.6969i	−0.472622	−	0.472622i	−0.902762	+	0.430140i	$0.858464\pi$
$968$	−10.1769	+	10.1769i	−0.327098	+	0.327098i
$969$		−	62.5692i		−	2.01001i
$970$		0			0
$971$		−	17.0941i		−	0.548575i	−0.961648	−	0.274288i	$-0.911558\pi$
$971$		−	17.0941i		−	0.548575i	0.961648	−	0.274288i	$-0.0884421\pi$
$972$		0			0
$973$	23.9874	+	23.9874i	0.769001	+	0.769001i
$974$			27.4641i			0.880007i
$975$		0			0
$976$			3.68886i			0.118078i
$977$	−14.1050	+	14.1050i	−0.451258	+	0.451258i	−0.895772	−	0.444514i	$-0.853376\pi$
$977$	−14.1050	+	14.1050i	−0.451258	+	0.451258i	0.444514	+	0.895772i	$0.353376\pi$
$978$	−19.9241	+	19.9241i	−0.637102	+	0.637102i
$979$		−	62.5692i		−	1.99972i
$980$		0			0
$981$		0			0
$982$	−3.20736	−	3.20736i	−0.102351	−	0.102351i
$983$	−19.1741	−	19.1741i	−0.611559	−	0.611559i	0.331793	−	0.943352i	$-0.392346\pi$
$983$	−19.1741	−	19.1741i	−0.611559	−	0.611559i	−0.943352	+	0.331793i	$0.892346\pi$
$984$			20.6603i			0.658625i
$985$		0			0
$986$			39.1713i			1.24747i
$987$	−12.3432	+	12.3432i	−0.392887	+	0.392887i
$988$	−16.8611	−	16.8611i	−0.536423	−	0.536423i
$989$	−0.988427	−	7.41154i	−0.0314302	−	0.235673i
$990$		0			0
$991$	50.1051			1.59164			0.795821	−	0.605532i	$-0.207040\pi$
$991$	50.1051			1.59164			0.795821	+	0.605532i	$0.207040\pi$
$992$	3.34607	+	3.34607i	0.106238	+	0.106238i
$993$	24.2311	−	24.2311i	0.768951	−	0.768951i
$994$	−2.28268			−0.0724021
$995$		0			0
$996$		−	27.8958i		−	0.883913i
$997$	23.4225	+	23.4225i	0.741797	+	0.741797i	0.972924	−	0.231127i	$-0.0742413\pi$
$997$	23.4225	+	23.4225i	0.741797	+	0.741797i	−0.231127	+	0.972924i	$0.574241\pi$
$998$	15.5563	−	15.5563i	0.492428	−	0.492428i
$999$	30.2345			0.956576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.f.1057.4	yes	16
5.2	odd	4	inner	1150.2.e.f.643.6	yes	16
5.3	odd	4	inner	1150.2.e.f.643.3	✓	16
5.4	even	2	inner	1150.2.e.f.1057.5	yes	16
23.22	odd	2	inner	1150.2.e.f.1057.3	yes	16
115.22	even	4	inner	1150.2.e.f.643.5	yes	16
115.68	even	4	inner	1150.2.e.f.643.4	yes	16
115.114	odd	2	inner	1150.2.e.f.1057.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.e.f.643.3	✓	16	5.3	odd	4	inner
1150.2.e.f.643.4	yes	16	115.68	even	4	inner
1150.2.e.f.643.5	yes	16	115.22	even	4	inner
1150.2.e.f.643.6	yes	16	5.2	odd	4	inner
1150.2.e.f.1057.3	yes	16	23.22	odd	2	inner
1150.2.e.f.1057.4	yes	16	1.1	even	1	trivial
1150.2.e.f.1057.5	yes	16	5.4	even	2	inner
1150.2.e.f.1057.6	yes	16	115.114	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 - 1.22474i) q^{3} +1.00000i q^{4} -1.73205 q^{6} +(1.50597 - 1.50597i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.22474 - 1.22474i) q^{3} +1.00000i q^{4} -1.73205 q^{6} +(1.50597 - 1.50597i) q^{7} +(0.707107 - 0.707107i) q^{8} +5.03908i q^{11} +(1.22474 + 1.22474i) q^{12} +(-3.34607 + 3.34607i) q^{13} -2.12976 q^{14} -1.00000 q^{16} +(5.06914 - 5.06914i) q^{17} +5.03908 q^{19} -3.68886i q^{21} +(3.56317 - 3.56317i) q^{22} +(3.80969 + 2.91312i) q^{23} -1.73205i q^{24} +4.73205 q^{26} +(3.67423 + 3.67423i) q^{27} +(1.50597 + 1.50597i) q^{28} -5.46410i q^{29} +4.73205 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.17158 + 6.17158i) q^{33} -7.16884 q^{34} +(4.11439 - 4.11439i) q^{37} +(-3.56317 - 3.56317i) q^{38} +8.19615i q^{39} -11.9282 q^{41} +(-2.60842 + 2.60842i) q^{42} +(-1.10245 - 1.10245i) q^{43} -5.03908 q^{44} +(-0.633975 - 4.75374i) q^{46} +(-3.34607 - 3.34607i) q^{47} +(-1.22474 + 1.22474i) q^{48} +2.46410i q^{49} -12.4168i q^{51} +(-3.34607 - 3.34607i) q^{52} +(9.73475 + 9.73475i) q^{53} -5.19615i q^{54} -2.12976i q^{56} +(6.17158 - 6.17158i) q^{57} +(-3.86370 + 3.86370i) q^{58} -0.535898i q^{59} -3.68886i q^{61} +(-3.34607 - 3.34607i) q^{62} -1.00000i q^{64} -8.72794i q^{66} +(-2.05719 + 2.05719i) q^{67} +(5.06914 + 5.06914i) q^{68} +(8.23373 - 1.09808i) q^{69} +1.07180 q^{71} +(0.568406 - 0.568406i) q^{73} -5.81863 q^{74} +5.03908i q^{76} +(7.58871 + 7.58871i) q^{77} +(5.79555 - 5.79555i) q^{78} +2.70043 q^{79} +9.00000 q^{81} +(8.43451 + 8.43451i) q^{82} +(-11.3884 - 11.3884i) q^{83} +3.68886 q^{84} +1.55910i q^{86} +(-6.69213 - 6.69213i) q^{87} +(3.56317 + 3.56317i) q^{88} -12.4168 q^{89} +10.0782i q^{91} +(-2.91312 + 3.80969i) q^{92} +(5.79555 - 5.79555i) q^{93} +4.73205i q^{94} +1.73205 q^{96} +(1.10245 - 1.10245i) q^{97} +(1.74238 - 1.74238i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 16 q^{16} + 48 q^{26} + 48 q^{31} - 80 q^{41} - 24 q^{46} + 128 q^{71} + 144 q^{81}+O(q^{100}) \) 16 * q - 16 * q^16 + 48 * q^26 + 48 * q^31 - 80 * q^41 - 24 * q^46 + 128 * q^71 + 144 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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